Notes on this puzzle
Fifteen #5104 is a 3×3 board with 8 numbered tiles and one gap, which starts in row 2, column 1. 3 tiles start in their home squares.
Add up how far each tile is from its home square and you get 9. 2 pairs of tiles already sit in their correct line but in the wrong order, which pushes the minimum to at least 13 moves. The shortest possible solution is exactly 19 moves. Matching it is a real achievement. Tile 8 has the longest trip home: 3 squares.
Where to beginOn the small board, think two or three moves ahead and look for short cycles that bring two tiles home together.